Killing Maths Mosquitoes with Atomic Proofs: roots of two, Fermat and prime numbers

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Stand-up Maths

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Published on October 23, 2015 5:15:59 PM ● Video Link: https://www.youtube.com/watch?v=W1OkVkq2vFM

Duration: 5:44

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How to prove that the roots of two are irrational using Fermat's Last Theory and that there are infinitely many primes using the Green-Tao theorem.

Yes, yes: Green and Tao took it as a given that there are infinitely many prime numbers and my pithy proof may very well be circular! If you wish to check, they're paper is here: http://annals.math.princeton.edu/wp-content/uploads/annals-v167-n2-p03.pdf

Actually, the point has been raised that even the Andrew Wiles proof of Fermat must contain the assumption that 2 is irrational, or something equivalent. If anyone can email me an Atomic Mosquito proof ( matt@standupmaths.com ) which does not contain any circular logic, I'll do a follow-up video.

This is PrimeGrid: http://www.primegrid.com/

If you missed them, here are the 26 primes which are all 5,283,234,035,979,900 apart:

43142746595714191
48425980631694091
53709214667673991
58992448703653891
64275682739633791
69558916775613691
74842150811593591
80125384847573491
85408618883553391
90691852919533291
95975086955513191
101258320991493091
106541555027472991
111824789063452891
117108023099432791
122391257135412691
127674491171392591
132957725207372491
138240959243352391
143524193279332291
148807427315312191
154090661351292091
159373895387271991
164657129423251891
169940363459231791
175223597495211691